How much federal taxes should I have withheld from a $50,000 cash prize. Also, how much state tax should I withhold? I live in Upstate NY.

I guess it is hard to tell; there is no way to say from the info provided. You ned to report the cash prize on line 21 of 1040.If you were in a 25% tax bracket the tax would be 25% of the prize, or more if it moved you to a higher tax bracket. Legally you pay on a $1 prize. So the $50K is taxable for both federal and state. When you receive income that is not subject to withholding,so you can adjust the taxes withheld by your employer If you are an employee, the Withholding Calculator can help you determine whether you need to give your employer a new Form W-4 to avoid having too much or too little Federal income tax withheld from your pay.you’d benefit From The Withholding Calculator as an Employee with non-wage income in excess of your adjustments and deductions, who would prefer to have tax on that income withheld from your paychecks rather than make periodic separate payments through the estimated tax procedures. you can visit the website here and follow step by step instructions; 2014 Withholding Calculator

For your NYS tax liability, You will actually pay at your marginal rate, which depends on the tax for the State you live in too. I don't kjnow your situation other than your cash prize, so I have attached links to New York depts' of revenue for you to look at;
Filing Information for New York State residents
or contact for more info on NYS taxation;

Telephone number infomation -- individuals

OR, you may pay estimated taxes.Estimated taxes are generally paid on income that is not subject to tax withholdings, or when tax withholdings are not sufficient to cover expected taxes on income.As income withholdings are uncommon von Prizes & Awards you may pay estimated taxes to IRS/State. Most employees who have federal and state income taxes, Medicare taxes, and Social Security withheld from income as part of payroll generally do not have to pay estimated taxes on that income. These withholdings can be seen at the end of the year on W-2 statements. However when an employee has additional sources of income, such as a cash prize or eetc , estimated tax payments may be required.